Finite Group Databasebeta

← C2×#19137663 #25256201

Subgroups — C2×#19137663 #25256201

Order 11008.

3678 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063311C211yesmaximal, characteristic
2C22×#13063290C211yesmaximal, characteristic, complemented
3C22×C4×C22⋊D43C211yesmaximal, characteristic
4#19137663C2116yesmaximal, direct product factor
5C2×#14582803C211yesmaximal, characteristic, complemented
6C2×#14582799C211yesmaximal, characteristic
7C2×#14582792C211yesmaximal, characteristic, complemented
8C2×#14582791C211yesmaximal, characteristic, complemented
9C2×#14582789C211yesmaximal, characteristic, complemented
10C2×#14582787C211yesmaximal, characteristic, complemented
11C2×#14582770C211yesmaximal, characteristic, complemented
12C2×C4⋊C4×Dic43C211yesmaximal, characteristic, complemented
13C2×#14582750C211yesmaximal, characteristic, complemented
14C2×C4×C22⋊Dic43C211yesmaximal, characteristic, complemented
15C2×#14582746C211yesmaximal, characteristic, complemented
16C2×C43×#385C211yesmaximal, characteristic, complemented
17C23×Dic86C2211yescharacteristic
18C23×C22⋊D43C2211yescharacteristic
19C23×C4×D43C2211yescharacteristic
20C2×#13063311C4116yescomplemented
21C2×#13063311C2218yes—
22C2×#13063290—28no—
23C2×#13063290C2218yescomplemented
24C2×C4×C22⋊D43—28no—
25C2×C4×C22⋊D43C2218yes—
26C22×C4⋊Dic43C2211yescharacteristic
27C22×Dic43⋊C4C2211yescharacteristic
28C22×Dic43⋊C4C2211yescharacteristic
29C22×Dic43⋊C4C2211yescharacteristic
30C22×C22⋊Dic43C2211yescharacteristic
31C22×C22⋊Dic43C2211yescharacteristic
32C22×C22⋊Dic43C2211yescharacteristic
33C22×(C2×D43)⋊C4C2211yescharacteristic
34C22×(C2×D43)⋊C4C2211yescharacteristic
35C22×(C2×D43)⋊C4C2211yescharacteristic
36C22×(C2×D43)⋊C4C2211yescharacteristic
37C22×(C2×D43)⋊C4C2211yescharacteristic
38C22×C4×Dic43C2211yescharacteristic
39C22×C4×Dic43C2211yescharacteristic
40C22×C4×Dic43C2211yescharacteristic
41C22×C4×Dic43C2211yescharacteristic
42C22×C4×Dic43C2211yescharacteristic
43C22×C4×Dic43C2211yescharacteristic
44C22×C4×Dic43C2211yescharacteristic
45#14582803C2218yescomplemented
46#14582799C2218yes—
47#14582792C2218yescomplemented
48#14582791C2218yescomplemented
49#14582789C2218yescomplemented
50#14582787C2218yescomplemented
51#14582770C2218yescomplemented
52C4⋊C4×Dic43C2218yescomplemented
53#14582750C2218yescomplemented
54C4×C22⋊Dic43C2218yescomplemented
55#14582746C2218yescomplemented
56C2×C43⋊#95C2211yescharacteristic
57C2×C43⋊#95C2211yescharacteristic
58C2×C43⋊#95C2211yescharacteristic
59C2×C43⋊#95C2211yescharacteristic
60C2×C43⋊#95C2211yescharacteristic
61C2×C43⋊#95C2211yescharacteristic
62C24×C4×C43C2211yescharacteristic
63C22×C4⋊C4×C43C2211yescharacteristic
64C22×C4⋊C4×C43C2211yescharacteristic
65C22×C22⋊C4×C43C2211yescharacteristic
66C22×C22⋊C4×C43C2211yescharacteristic
67C43×#385C2218yescomplemented
68C2×#95×C43C2211yescharacteristic
69C2×#95×C43C2211yescharacteristic
70C24×D43C2311yescharacteristic
71C22×Dic86—24no—
72C22×Dic86—24no—
73C22×Dic86C2×C418yescomplemented
74C22×Dic86C2314yes—
75C22×C22⋊D43—24no—
76C22×C22⋊D43—24no—
77C22×C22⋊D43C2×C418yes—
78C22×C22⋊D43C2314yes—
79C23×Dic43C2311yescharacteristic
80C23×Dic43C2311yescharacteristic
81C23×Dic43C2311yescharacteristic
82C23×Dic43C2311yescharacteristic
83C23×Dic43C2311yescharacteristic
84C23×Dic43C2311yescharacteristic
85C23×Dic43C2311yescharacteristic
86C22×C4×D43—24no—
87C22×C4×D43—24no—
88C22×C4×D43—42no—
89C22×C4×D43C2314yes—
90#13063311C2×C4164yescomplemented
91#13063290—232no—
92C4×C22⋊D43—232no—
93C2×C4⋊Dic43—24no—
94C2×C4⋊Dic43C2314yes—
95C2×Dic43⋊C4—24no—
96C2×Dic43⋊C4—24no—
97C2×Dic43⋊C4D418yes—
98C2×Dic43⋊C4C2314yes—
99C2×Dic43⋊C4C2314yes—
100C2×Dic43⋊C4C2314yes—
101C2×C22⋊Dic43—24no—
102C2×C22⋊Dic43—24no—
103C2×C22⋊Dic43C2×C418yescomplemented
104C2×C22⋊Dic43C2314yes—
105C2×C22⋊Dic43C2314yes—
106C2×C22⋊Dic43C2314yes—
107C2×(C2×D43)⋊C4—24no—
108C2×(C2×D43)⋊C4—24no—
109C2×(C2×D43)⋊C4—42no—
110C2×(C2×D43)⋊C4C2×C418yescomplemented
111C2×(C2×D43)⋊C4C2×C418yescomplemented
112C2×(C2×D43)⋊C4C2314yes—
113C2×(C2×D43)⋊C4C2314yes—
114C2×(C2×D43)⋊C4C2314yes—
115C2×(C2×D43)⋊C4C2314yes—
116C2×(C2×D43)⋊C4C2314yes—
117C2×C4×Dic43—24no—
118C2×C4×Dic43—24no—
119C2×C4×Dic43—24no—
120C2×C4×Dic43—24no—
121C2×C4×Dic43—42no—
122C2×C4×Dic43—42no—
123C2×C4×Dic43C2×C418yescomplemented
124C2×C4×Dic43C2314yes—
125C2×C4×Dic43C2314yes—
126C2×C4×Dic43C2314yes—
127C2×C4×Dic43C2314yes—
128C2×C4×Dic43C2314yes—
129C2×C4×Dic43C2314yes—
130C2×C4×Dic43C2314yes—
131C43⋊#95C2314yes—
132C43⋊#95C2314yes—
133C43⋊#95C2314yes—
134C43⋊#95C2314yes—
135C43⋊#95C2314yes—
136C43⋊#95C2314yes—
137C25×C43C2311yescharacteristic
138C23×C4×C43—24no—
139C23×C4×C43—24no—
140C23×C4×C43—42no—
141C23×C4×C43C2311yescharacteristic
142C23×C4×C43C2311yescharacteristic
143C23×C4×C43C2314yes—
144C23×C4×C43C2311yescharacteristic
145C23×C4×C43C2311yescharacteristic
146C23×C4×C43C2311yescharacteristic
147C23×C4×C43C2311yescharacteristic
148C2×C4⋊C4×C43—24no—
149C2×C4⋊C4×C43—24no—
150C2×C4⋊C4×C43C2314yes—
151C2×C4⋊C4×C43C2314yes—
152C2×C22⋊C4×C43—42no—
153C2×C22⋊C4×C43C2×C418yescomplemented
154C2×C22⋊C4×C43C2314yes—
155C2×C22⋊C4×C43C2314yes—
156#95×C43C2314yes—
157#95×C43C2314yes—
158C24×C43—22no—
159C24×C43—22no—
160C24×C43—22no—
161C24×C43—22no—
162C24×C43—22no—
163C24×C43—22no—
164C24×C43C22×C414yes—
165C24×C43C2412yes—
166C24×C43C2411yescharacteristic
167C23×D43—22no—
168C23×D43—22no—
169C23×D43—22no—
170C23×D43—22no—
171C23×D43—22no—
172C23×D43—22no—
173C23×D43C22×C414yes—
174C23×D43C2412yes—
175C22×C4×C43—28no—
176C22×C4×C43—28no—
177C22×C4×C43—22no—
178C22×C4×C43—22no—
179C22×C4×C43—22no—
180C22×C4×C43—22no—
181C22×C4×C43—22no—
182C22×C4×C43—22no—
183C22×C4×C43—22no—
184C22×C4×C43—22no—
185C22×C4×C43—22no—
186C22×C4×C43—22no—
187C22×C4×C43—22no—
188C22×C4×C43—22no—
189C22×C4×C43—22no—
190C22×C4×C43—22no—
191C22×C4×C43—44no—
192C22×C4×C43—416no—
193C22×C4×C43C22×C414yes—
194C22×C4×C43C22×C414yes—
195C22×C4×C43C2×D414yes—
196C22×C4×C43#4114yes—
197C22×C4×C43C2412yes—
198C22×C4×C43C2412yes—
199C22×C4×C43C2412yes—
200C22×C4×C43C2412yes—
201C22×C4×C43C2412yes—
202C22×C4×C43C2412yes—
203C2×C22⋊D43—232no—
204C2×C22⋊D43—28no—
205C2×C22⋊D43—28no—
206C2×C22⋊D43C22×C4116yes—
207C22×Dic43—22no—
208C22×Dic43—22no—
209C22×Dic43—22no—
210C22×Dic43—22no—
211C22×Dic43—22no—
212C22×Dic43—22no—
213C22×Dic43—22no—
214C22×Dic43—22no—
215C22×Dic43—22no—
216C22×Dic43—22no—
217C22×Dic43—22no—
218C22×Dic43—22no—
219C22×Dic43—22no—
220C22×Dic43—22no—
221C22×Dic43C22×C414yes—
222C22×Dic43C22×C414yes—
223C22×Dic43C22×C414yes—
224C22×Dic43C2×D414yes—
225C22×Dic43C2×D414yes—
226C22×Dic43#4114yes—
227C22×Dic43#4114yes—
228C22×Dic43C2412yes—
229C22×Dic43C2412yes—
230C22×Dic43C2412yes—
231C22×Dic43C2412yes—
232C22×Dic43C2412yes—
233C22×Dic43C2412yes—
234C22×Dic43C2412yes—
235C2×C4×D43—28no—
236C2×C4×D43—28no—
237C2×C4×D43—44no—
238C2×C4×D43—416no—
239C2×Dic86—232no—
240C2×Dic86—28no—
241C2×Dic86—28no—
242C2×Dic86C22×C4116yescomplemented
243C4⋊C4×C43—28no—
244C4⋊C4×C43—28no—
245C22⋊C4×C43—44no—
246C22⋊C4×C43C22×C4116yescomplemented
247C22⋊Dic43—28no—
248C22⋊Dic43—28no—
249C22⋊Dic43C22×C4116yescomplemented
250(C2×D43)⋊C4—28no—
251(C2×D43)⋊C4—28no—
252(C2×D43)⋊C4—44no—
253(C2×D43)⋊C4C22×C4116yescomplemented
254(C2×D43)⋊C4C22×C4116yescomplemented
255C4⋊Dic43—28no—
256Dic43⋊C4—28no—
257Dic43⋊C4—28no—
258Dic43⋊C4C2×D4116yes—
259C4×Dic43—28no—
260C4×Dic43—28no—
261C4×Dic43—28no—
262C4×Dic43—28no—
263C4×Dic43—44no—
264C4×Dic43—44no—
265C4×Dic43C22×C4116yescomplemented
266C23×C43—28no—
267C23×C43—28no—
268C23×C43—28no—
269C23×C43—22no—
270C23×C43—22no—
271C23×C43—22no—
272C23×C43—22no—
273C23×C43—22no—
274C23×C43—22no—
275C23×C43—44no—
276C23×C43—44no—
277C23×C43—44no—
278C23×C43—44no—
279C23×C43C23×C414yes—
280C23×C43C23×C412yes—
281C23×C43C22×D412yes—
282C23×C43C2×#4112yes—
283C23×C43C2×#4112yes—
284C23×C43C2×#4112yes—
285C23×C43H(5,𝔽2)12yes—
286C23×C432−1+412yes—
287C23×C43C2511yescharacteristic
288C22×D43—28no—
289C22×D43—28no—
290C22×D43—28no—
291C22×D43—22no—
292C22×D43—22no—
293C22×D43—22no—
294C22×D43—22no—
295C22×D43—22no—
296C22×D43—22no—
297C22×D43—44no—
298C22×D43—44no—
299C22×D43—44no—
300C22×D43—44no—
301C22×D43C23×C414yes—
302C2×C4×C43—28no—
303C2×C4×C43—28no—
304C2×C4×C43—28no—
305C2×C4×C43—28no—
306C2×C4×C43—22no—
307C2×C4×C43—22no—
308C2×C4×C43—22no—
309C2×C4×C43—22no—
310C2×C4×C43—22no—
311C2×C4×C43—22no—
312C2×C4×C43—22no—
313C2×C4×C43—22no—
314C2×C4×C43—22no—
315C2×C4×C43—22no—
316C2×C4×C43—22no—
317C2×C4×C43—22no—
318C2×C4×C43—22no—
319C2×C4×C43—22no—
320C2×C4×C43—416no—
321C2×C4×C43—44no—
322C2×C4×C43—44no—
323C2×C4×C43C23×C414yes—
324C2×C4×C43C23×C414yes—
325C2×C4×C43C22×D414yes—
326C2×C4×C43C2×#4114yes—
327C22⋊D43—232no—
328C2×Dic43—28no—
329C2×Dic43—28no—
330C2×Dic43—28no—
331C2×Dic43—28no—
332C2×Dic43—22no—
333C2×Dic43—22no—
334C2×Dic43—22no—
335C2×Dic43—22no—
336C2×Dic43—22no—
337C2×Dic43—22no—
338C2×Dic43—22no—
339C2×Dic43—22no—
340C2×Dic43—22no—
341C2×Dic43—22no—
342C2×Dic43—22no—
343C2×Dic43—22no—
344C2×Dic43—22no—
345C2×Dic43—22no—
346C2×Dic43—44no—
347C2×Dic43—44no—
348C2×Dic43C4×D4116yes—
349C2×Dic43C23×C414yes—
350C2×Dic43C23×C414yes—
351C2×Dic43C23×C414yes—
352C2×Dic43C22×D414yes—
353C2×Dic43C22×D414yes—
354C2×Dic43C2×#4114yes—
355C2×Dic43C2×#4114yes—
356C4×D43—416no—
357Dic86—232no—
358C2×#2367—431nomaximal, Sylow
359C22×C43—24no—
360C22×C43—24no—
361C22×C43—24no—
362C22×C43—416no—
363C22×C43—42no—
364C22×C43—42no—
365C22×C43—42no—
366C22×C43—42no—
367C22×C43C2×C4×D414yes—
368C22×C43C4×#4114yes—
369C22×C43#52014yes—
370C22×C43#54614yes—
371C22×C43#54814yes—
372C22×C43#55614yes—
373C22×C43#55914yes—
374C22×C43C24×C411yescharacteristic
375C22×C43C23×D411yescharacteristic
376C22×C43C22×#4111yescharacteristic
377C22×C43C22×#4111yescharacteristic
378C22×C43C22×#4111yescharacteristic
379C22×C43C2×H(5,𝔽2)11yescharacteristic
380C22×C43C2×2−1+411yescharacteristic
381C2×D43—24no—
382C2×D43—24no—
383C2×D43—24no—
384C2×D43—416no—
385C2×D43—42no—
386C2×D43—42no—
387C2×D43—42no—
388C2×D43—42no—
389C4×C43—24no—
390C4×C43—24no—
391C4×C43—24no—
392C4×C43—24no—
393C4×C43—42no—
394C4×C43—42no—
395Dic43—24no—
396Dic43—24no—
397Dic43—24no—
398Dic43—24no—
399Dic43—42no—
400Dic43—42no—
401Dic43C2×C4×D418yes—
402C22×#124—431no—
403C22×C4×Q8—431no—
404C22×C4×D4—431no—
405#2367—4316no—
406C2×#391—431no—
407C2×#390—431no—
408C2×#388—431no—
409C2×#388—431no—
410C2×#388—431no—
411C2×#388—431no—
412C2×#385—431no—
413C2×#385D4311yescharacteristic, complemented
414C2×C4×C4⋊C4—431no—
415C2×C4×C4⋊C4—431no—
416C2×C4×C22⋊C4—431no—
417C2×C4×C22⋊C4—431no—
418C2×C43—44no—
419C2×C43#236718yescomplemented
420C2×C43C22×C4×D411yescharacteristic
421C2×C43C2×C4×#4111yescharacteristic
422C2×C43C2×#52011yescharacteristic
423C2×C43C2×#54611yescharacteristic
424C2×C43C2×#54811yescharacteristic
425C2×C43C2×#55611yescharacteristic
426C2×C43C2×#55911yescharacteristic
427D43—44no—
428C23×Q8—431no—
429C23×D4—431no—
430C24×C4—431no—
431C24×C4C2×D4311yescharacteristic
432C2×#124—438no—
433C2×#124—4316no—
434C2×C4×Q8—438no—
435C2×C4×Q8—868no—
436C2×C4×D4—438no—
437C2×C4×D4—868no—
438C22×C4⋊C4—431no—
439C22×C4⋊C4—431no—
440C22×C4⋊C4—431no—
441C22×C4⋊C4—431no—
442C22×C4⋊C4C2×D4311yescharacteristic
443C22×C4⋊C4C2×D4311yescharacteristic
444C22×C22⋊C4—431no—
445C22×C22⋊C4—431no—
446C22×C22⋊C4—431no—
447C22×C22⋊C4—431no—
448C22×C22⋊C4—431no—
449C22×C22⋊C4—431no—
450C22×C22⋊C4—431no—
451C22×C22⋊C4—431no—
452C22×C22⋊C4C2×D4311yescharacteristic
453C22×C22⋊C4C2×D4311yescharacteristic
454C22×C42—431no—
455C22×C42—431no—
456C22×C42—431no—
457C22×C42—431no—
458C22×C42—431no—
459C22×C42—431no—
460C22×C42—431no—
461#391—438no—
462#390—438no—
463#388—438no—
464#388—438no—
465#388—438no—
466#388—438no—
467#385—438no—
468#385C2×D4318yescomplemented
469C4×C4⋊C4—438no—
470C4×C4⋊C4—438no—
471C4×C22⋊C4—438no—
472C4×C22⋊C4—438no—
473C2×#95—431no—
474C2×#95—431no—
475C2×#95—431no—
476C2×#95—431no—
477C2×#95—431no—
478C2×#95—431no—
479C2×#95C2×D4311yescharacteristic
480C2×#95C2×D4311yescharacteristic
481C43C2×#236711yescharacteristic, complemented, Sylow
482C25—431no—
483C25C22×D4311yescharacteristic
484C22×Q8—438no—
485C22×Q8—434no—
486C22×Q8—864no—
487C22×Q8—864no—
488C22×D4—438no—
489C22×D4—434no—
490C22×D4—864no—
491C22×D4—864no—
492C23×C4—24no—
493C23×C4—24no—
494C23×C4—42no—
495C23×C4—431no—
496C23×C4—431no—
497C23×C4—431no—
498C23×C4—431no—
499C23×C4—431no—
500C23×C4—431no—
501C23×C4—431no—
502C23×C4—434no—
503C23×C4—864no—
504C23×C4—864no—
505C23×C4—1722no—
506C23×C4C22×D4311yescharacteristic
507C23×C4C22×D4311yescharacteristic
508C23×C4C22×D4314yes—
509C23×C4C22×D4311yescharacteristic
510C23×C4C22×D4311yescharacteristic
511C23×C4C22×D4311yescharacteristic
512C23×C4C22×D4311yescharacteristic
513#124—4364no—
514C4×Q8—8632no—
515C4×D4—8632no—
516C2×C4⋊C4—24no—
517C2×C4⋊C4—24no—
518C2×C4⋊C4—438no—
519C2×C4⋊C4—434no—
520C2×C4⋊C4—434no—
521C2×C4⋊C4—434no—
522C2×C4⋊C4—434no—
523C2×C4⋊C4—864no—
524C2×C4⋊C4—864no—
525C2×C4⋊C4—864no—
526C2×C4⋊C4C22×D4314yes—
527C2×C4⋊C4C22×D4314yes—
528C2×C22⋊C4—42no—
529C2×C22⋊C4—438no—
530C2×C22⋊C4—434no—
531C2×C22⋊C4—438no—
532C2×C22⋊C4—438no—
533C2×C22⋊C4—434no—
534C2×C22⋊C4—434no—
535C2×C22⋊C4—434no—
536C2×C22⋊C4—434no—
537C2×C22⋊C4—434no—
538C2×C22⋊C4—434no—
539C2×C22⋊C4—434no—
540C2×C22⋊C4—864no—
541C2×C22⋊C4—864no—
542C2×C22⋊C4—864no—
543C2×C22⋊C4—864no—
544C2×C22⋊C4—1722no—
545C2×C22⋊C4C4×D4318yescomplemented
546C2×C22⋊C4C22×D4314yes—
547C2×C22⋊C4C22×D4314yes—
548C2×C42—438no—
549C2×C42—434no—
550C2×C42—434no—
551C2×C42—434no—
552C2×C42—434no—
553C2×C42—434no—
554C2×C42—434no—
555C2×C42—434no—
556C2×C42—864no—
557C2×C42—864no—
558C2×C42—864no—
559C2×C42—864no—
560C2×C42—1722no—
561C2×C42—1722no—
562#95—434no—
563#95—434no—
564#95—434no—
565#95—434no—
566#95—434no—
567#95—434no—
568#95C22×D4314yes—
569#95C22×D4314yes—
570C24—22no—
571C24—22no—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—434no—
577C24—432no—
578C24—862no—
579C24—862no—
580C24—862no—
581C24—862no—
582C24—862no—
583C24—862no—
584C24C2×C4×D4314yes—
585C24C23×D4312yes—
586C24C23×D4311yescharacteristic
587C2×Q8—4316no—
588C2×Q8—868no—
589C2×Q8—8632no—
590C2×Q8—868no—
591C2×D4—4316no—
592C2×D4—868no—
593C2×D4—8632no—
594C2×D4—868no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—28no—
610C22×C4—28no—
611C22×C4—44no—
612C22×C4—416no—
613C22×C4—434no—
614C22×C4—434no—
615C22×C4—434no—
616C22×C4—432no—
617C22×C4—434no—
618C22×C4—434no—
619C22×C4—434no—
620C22×C4—434no—
621C22×C4—432no—
622C22×C4—432no—
623C22×C4—432no—
624C22×C4—432no—
625C22×C4—432no—
626C22×C4—432no—
627C22×C4—868no—
628C22×C4—862no—
629C22×C4—862no—
630C22×C4—862no—
631C22×C4—862no—
632C22×C4—862no—
633C22×C4—862no—
634C22×C4—862no—
635C22×C4—862no—
636C22×C4—862no—
637C22×C4—862no—
638C22×C4—862no—
639C22×C4—862no—
640C22×C4—862no—
641C22×C4—862no—
642C22×C4—868no—
643C22×C4—1724no—
644C22×C4—17216no—
645C22×C4C2×C4×D4314yes—
646C22×C4C2×C4×D4314yes—
647C22×C4D4×D4314yes—
648C22×C4#1062190014yes—
649C22×C4C23×D4312yes—
650C22×C4C23×D4312yes—
651C22×C4C23×D4312yes—
652C22×C4C23×D4312yes—
653C22×C4C23×D4312yes—
654C22×C4C23×D4312yes—
655C4⋊C4—28no—
656C4⋊C4—28no—
657C4⋊C4—4316no—
658C4⋊C4—868no—
659C4⋊C4—868no—
660C4⋊C4—868no—
661C22⋊C4—44no—
662C22⋊C4—4316no—
663C22⋊C4—4316no—
664C22⋊C4—4316no—
665C22⋊C4—868no—
666C22⋊C4—868no—
667C22⋊C4—868no—
668C22⋊C4—868no—
669C22⋊C4—1724no—
670C22⋊C4C2×C4×D43116yescomplemented
671C42—4316no—
672C42—868no—
673C42—868no—
674C42—868no—
675C42—868no—
676C42—1724no—
677C42—1724no—
678C23—28no—
679C23—28no—
680C23—28no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—44no—
688C23—44no—
689C23—44no—
690C23—44no—
691C23—434no—
692C23—868no—
693C23—868no—
694C23—868no—
695C23—862no—
696C23—862no—
697C23—862no—
698C23—862no—
699C23—862no—
700C23—862no—
701C23—1724no—
702C23—1724no—
703C23—1724no—
704C23—1724no—
705C23C22×C4×D4314yes—
706C23C22×C4×D4312yes—
707C23C2×D4×D4312yes—
708C23#41×D4312yes—
709C23#41×D4312yes—
710C23C2×#1062190012yes—
711C23#1306337012yes—
712C23#1306337312yes—
713C23C24×D4311yescharacteristic
714Q8—8632no—
715D4—8632no—
716C2×C4—28no—
717C2×C4—28no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—28no—
727C2×C4—28no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—416no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—4316no—
738C2×C4—434no—
739C2×C4—434no—
740C2×C4—434no—
741C2×C4—434no—
742C2×C4—434no—
743C2×C4—434no—
744C2×C4—434no—
745C2×C4—868no—
746C2×C4—868no—
747C2×C4—868no—
748C2×C4—862no—
749C2×C4—862no—
750C2×C4—862no—
751C2×C4—862no—
752C2×C4—862no—
753C2×C4—862no—
754C2×C4—862no—
755C2×C4—862no—
756C2×C4—868no—
757C2×C4—862no—
758C2×C4—862no—
759C2×C4—862no—
760C2×C4—862no—
761C2×C4—862no—
762C2×C4—862no—
763C2×C4—17216no—
764C2×C4—1724no—
765C2×C4—1724no—
766C2×C4C22×C4×D4314yes—
767C2×C4C22×C4×D4314yes—
768C2×C4C2×D4×D4314yes—
769C2×C4C2×#1062190014yes—
770C22—24no—
771C22—24no—
772C22—24no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—416no—
777C22—42no—
778C22—864no—
779C22—864no—
780C22—864no—
781C22—1722no—
782C22—1722no—
783C22—1722no—
784C22—17216no—
785C22—1722no—
786C22C4×D4×D4314yes—
787C22C4×#1062190014yes—
788C22#1458338014yes—
789C22#1458353614yes—
790C22#1458355914yes—
791C22#1458362014yes—
792C22#1458363314yes—
793C22C23×C4×D4311yescharacteristic
794C22C22×D4×D4311yescharacteristic
795C22C2×#41×D4311yescharacteristic
796C22C2×#41×D4311yescharacteristic
797C22C22×#1062190011yescharacteristic
798C22C2×#1306337011yescharacteristic
799C22C2×#1306337311yescharacteristic
800C4—24no—
801C4—24no—
802C4—24no—
803C4—24no—
804C4—42no—
805C4—42no—
806C4—438no—
807C4—864no—
808C4—864no—
809C4—864no—
810C4—864no—
811C4—1722no—
812C4—1722no—
813C2—44no—
814C2—1724no—
815C2#1913766318yesdirect product factor
816C2C2×C4×D4×D4311yescharacteristic
817C2C2×C4×#1062190011yescharacteristic
818C2C2×#1458338011yescharacteristic
819C2C2×#1458353611yescharacteristic
820C2C2×#1458355911yescharacteristic
821C2C2×#1458362011yescharacteristic
822C2C2×#1458363311yescharacteristic
subgroupG/H
centerC24C23×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC2×C43×#385C2
socleC24×C43C24
prime radicalC23×C22⋊D43C22
cosocleC23×C43C25
hypercenterC2×#385D43
hypocenterC43C2×#2367
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#385

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C22×#13063290C2semidirect
4. #19137663C2direct (N × H)
5. C2×#14582803C2semidirect
7. C2×#14582792C2semidirect
8. C2×#14582791C2semidirect
9. C2×#14582789C2semidirect
10. C2×#14582787C2semidirect
11. C2×#14582770C2semidirect
12. C2×C4⋊C4×Dic43C2semidirect
13. C2×#14582750C2semidirect
14. C2×C4×C22⋊Dic43C2semidirect
15. C2×#14582746C2semidirect
16. C2×C43×#385C2semidirect
20. C2×#13063311C4semidirect
23. C2×#13063290C22semidirect
45. #14582803C22semidirect
47. #14582792C22semidirect
48. #14582791C22semidirect
49. #14582789C22semidirect
50. #14582787C22semidirect
51. #14582770C22semidirect
52. C4⋊C4×Dic43C22semidirect
53. #14582750C22semidirect
54. C4×C22⋊Dic43C22semidirect
55. #14582746C22semidirect
67. C43×#385C22semidirect
73. C22×Dic86C2×C4semidirect
90. #13063311C2×C4semidirect
103. C2×C22⋊Dic43C2×C4semidirect
110. C2×(C2×D43)⋊C4C2×C4semidirect
111. C2×(C2×D43)⋊C4C2×C4semidirect
123. C2×C4×Dic43C2×C4semidirect
153. C2×C22⋊C4×C43C2×C4semidirect
242. C2×Dic86C22×C4semidirect
246. C22⋊C4×C43C22×C4semidirect
249. C22⋊Dic43C22×C4semidirect
253. (C2×D43)⋊C4C22×C4semidirect
254. (C2×D43)⋊C4C22×C4semidirect
265. C4×Dic43C22×C4semidirect
413. C2×#385D43semidirect
419. C2×C43#2367semidirect
468. #385C2×D43semidirect
481. C43C2×#2367semidirect
545. C2×C22⋊C4C4×D43semidirect
670. C22⋊C4C2×C4×D43semidirect
815. C2#19137663direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×#130633112
C22×#130632902
C22×C4×C22⋊D432
#191376632
C2×#145828032
C2×#145827992
C2×#145827922
C2×#145827912
C2×#145827892
C2×#145827872
C2×#145827702
C2×C4⋊C4×Dic432
C2×#145827502
C2×C4×C22⋊Dic432
C2×#145827462
C2×C43×#3852
C2×#236743